Nonlinear pulse propagation in single-mode inhomogeneous dielectric waveguides is analyzed by means of the reductive perturbation method. The chromatic dispersion of the fiber takes impurity-related resonance phenomena into account, while the nonlinear properties are described by means of a time- (frequency-) dependent dielectric constant with cubic nonlinearity. For the case of short-envelope propagation, a perturbed nonlinear Schrodinger equation, reflecting higher-order linear and nonlinear effects, is derived and then transformed into a generalized higher-order nonlinear Schrodinger (GHONLS) equation that is valid for both the anomalous- and the normal-dispersion regimes. In the search for quasi-stationary-wave solutions the GHONLS equation is then reduced to a nonlinear ordinary differential equation, which is analyzed by phase-space analysis. The latter leads to bright- and dark-soliton solutions that can be analytically derived and correspond to separatrices on the phase plane of the associated dynamical system. Emphasis is given to the connections among the initial spatiotemporal pulse information and the types of mode (bright or dark solitons) that can be excited.
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